How Synthetic Control Algorithms Build Counterfactuals to Measure Policy Outcomes

When a state legislature or central bank introduces a novel policy, economists cannot run a randomized trial to see what would have happened otherwise. The next time a government passes a unique tax or health mandate, evaluators will not rely on crude before-and-after comparisons. Instead, they will construct a mathematical phantom—a weighted combination of unaffected regions that perfectly mimics the treated area before the intervention—to measure the exact divergence between reality and the counterfactual.[4]

In 2003, economists Alberto Abadie and Javier Gardeazabal introduced a mathematical solution to this exact problem: the synthetic control method. Rather than comparing a treated region to a single flawed control region, or to a crude average of all untreated regions, the algorithm builds a bespoke synthetic twin. It does this by finding a weighted combination of untreated units—known as the donor pool—that perfectly mimics the treated unit's characteristics and trajectory in the years leading up to the intervention.[2]

The mechanics of the algorithm rely on a convex combination. The weights assigned to the donor units must be non-negative and sum exactly to one. This mathematical constraint prevents the model from extrapolating outside the bounds of the observed data. If the algorithm can successfully construct a synthetic twin that tightly tracks the real region for a decade before the policy change, any divergence between the two lines after the policy takes effect represents the causal impact of the intervention.[4]

The foundational demonstration of this technique measured the economic damage of terrorism in the Basque Country. Abadie and Gardeazabal gathered economic data from 1955 to 1969, before the conflict escalated in 1970. They fed 16 other Spanish regions into the algorithm to serve as the donor pool. The model discarded 14 of them entirely, assigning them a weight of zero. Instead, it built "Synthetic Basque" almost entirely from two regions: Catalonia, which received an 85.1% weight, and Madrid, which received 14.9%.[2]

By tracking this synthetic region forward in time, the researchers found a stark divergence. While the real Basque Country's economy suffered, the synthetic counterfactual continued to grow. The gap revealed that the conflict cost the region roughly an 8% income shortfall, peaking at a loss of $1,036 per capita in 1989. Because the synthetic control matched the real region so closely before 1970, the subsequent drop could be confidently attributed to the conflict rather than broader Spanish economic trends.[2]

The method gained widespread prominence following a 2010 study evaluating California's Proposition 99, a 1988 initiative that increased the state cigarette tax by 25 cents per pack and funded anti-smoking campaigns. National smoking rates were already declining, making it difficult to isolate the policy's specific effect using traditional regressions. The researchers provided the algorithm with a donor pool of 38 US states that had not implemented similar tobacco controls.[1]

Once again, the algorithm proved highly selective. It ignored 33 states entirely. The "Synthetic California" was composed of just five states, heavily dominated by Utah, which received a 33.4% weight. This mathematical phantom matched California's pre-1988 cigarette sales with an R-squared of 0.974, indicating a near-perfect fit. After the tax took effect in 1989, the real California's sales plummeted far faster than the synthetic model's.[1]

The data revealed that Proposition 99 reduced California's cigarette consumption by an average of 19.0 packs per capita per year over the following decade. By the year 2000, the gap had widened to 26.4 packs per capita—a 38% reduction relative to what the state would have consumed without the legislation. The precision of the synthetic control allowed researchers to prove that the tax was responsible for the decline, rather than shifting national attitudes.[1][4]

In 2015, the technique was scaled up to evaluate the macroeconomic impact of the 1990 German reunification. Using a donor pool of 16 OECD countries, the algorithm constructed a "Synthetic West Germany" to model what the nation's economy would have looked like had the Berlin Wall never fallen. The analysis demonstrated that over the 13 years following reunification, West Germany's GDP per capita was $1,600 lower each year than it would have been in the absence of the merger.[3]

Because synthetic controls rely on a single treated unit, traditional statistical significance tests—like standard errors or p-values—cannot be calculated. As economist Scott Cunningham notes in his causal inference text, "Synthetic controls models, at their core, are explicit imputation estimators that estimate what would have happened to a treated unit or units had some intervention never occurred." To solve the inference problem, researchers use in-space placebo tests. The algorithm is iteratively applied to every untreated unit in the donor pool, pretending that each one received the intervention. This creates a distribution of placebo effects.[1][2]

In the California tobacco study, the researchers ran the algorithm on all 38 donor states. California's post-treatment drop in cigarette sales was the most extreme of any state in the pool, yielding a pseudo p-value of 0.026. This permutation testing provides a robust, data-driven way to verify that the observed divergence is not just random noise. The next frontier for the methodology lies in adapting the algorithm to handle multiple treated units simultaneously, allowing researchers to evaluate staggered policy rollouts across different regions over time.[1][4]